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1794299a6c
Systematic native_decide → dec_trivial/rfl migration across all Lean modules to comply with AGENTS.md rule 5 (no native_decide unless only option): - CoreFormalism: BraidEigensolid, BraidField, ChentsovFinite, HachimojiBase, HachimojiBridging, HachimojiCodec, HachimojiLUT, HachimojiManifoldAxiom, Q16_16Numerics - BindingSite: BindingSiteCodec, BindingSiteEntropy, BindingSiteHachimoji - SilverSight: ProductSchema, ProductWireFormat, PolyFactorIdentity, Schema, WireFormat - PVGS_DQ_Bridge: all three files (native_decide->dec_trivial) - UniversalEncoding/ChiralitySpace Additional changes: - gemma4_mcp.py: upgraded to two-tier routing (local Gemma4 + FreeLLMAPI proxy) - ChentsovFinite: added traceability map and Chentsov (1972) citation - HachimojiBase: renamed Σ→Sig, Π→Pi to avoid non-ASCII issues - Import path fixes for Mathlib 4.30.0-rc2 compatibility - Doc updates: PURE_FORMULAS, SOS_CERTIFICATE, fundamental math derivations - Build log: 2026-06-26 session findings - BRKGLASS_NR_BRACKET_PROPOSAL: updated to REAL-DATA VALIDATED status - New docs: FOUNDATIONAL_GUIDANCE, PURE_EQUATION_MAP, CHENTSOV_FINITE_MATH, BREAKGLASS_FUSION_REVIEW_SPEC, COLD_REVIEWER_FORMULA - New python: phi pipeline (equation_dna_encoder, ast_parse, charclass, consistency, embed, output), nr_bracket_validation with receipt Build: lake build SilverSightRRC — passes on all committed modules. Excluded: HachimojiN8Bridge, HachimojiCharClass (missing CoreFormalism.HachimojiManifoldAxiom olean — WIP)
130 lines
3.6 KiB
Markdown
130 lines
3.6 KiB
Markdown
# Cold Reviewer Formula
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**Protocol for independent verification of the Unified Covariant Field Theory**
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A reviewer needs only a calculator and this checklist. No knowledge of Lean,
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braid theory, or Temperley–Lieb algebras is required to pass the arithmetic
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and structural gates.
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---
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## Arithmetic Gate
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Verify the following four invariants independently.
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### I₁. Golden-ratio identity
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\[
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\phi = \frac{1 + \sqrt{5}}{2}, \qquad \phi^2 - \phi - 1 = 0.
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\]
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*Check:* Compute \(\phi^2\), subtract \(\phi + 1\), obtain 0.
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### I₂. Fixed-point gap
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\[
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\sigma = \frac{9984}{65536} = \frac{39}{256}, \qquad
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\tau = \frac{1}{7},
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\]
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\[
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\sigma - \tau = \frac{39}{256} - \frac{1}{7}
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= \frac{273 - 256}{1792}
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= \frac{17}{1792} > 0.
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\]
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*Check:* Common denominator 1792. Numerator \(273 - 256 = 17 > 0\).
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### I₃. Fibonacci values
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\[
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F_7 = 13, \qquad F_8 = 21.
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\]
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*Check:* Run the recurrence \(F_0=0,\;F_1=1,\;F_{n+2}=F_{n+1}+F_n\) to term 8.
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### I₄. Binary / Sidon uniqueness
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For \(a,b,c,d \in \{0,\dots,7\}\),
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\[
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2^a + 2^b = 2^c + 2^d \;\Longrightarrow\; \{a,b\} = \{c,d\}.
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\]
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*Reason:* Binary expansion of integers is unique. A sum of two powers of two
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has either one bit set (\(a=b\), yielding \(2^{a+1}\)) or exactly two bits set
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(\(a \neq b\)). Equality therefore forces the same exponent multiset.
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---
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## Structural Gate
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Ensure the manuscript does **not** make any of the following claims.
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### Red Flag 1 — Wrong endomorphism relation
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| ✗ Prohibited | ✓ Correct |
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| \(J^2 = -I\) | \(J^2 = J + I\) |
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where \(J = \phi \cdot \mathrm{id}_V\). This operator satisfies the
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golden-ratio polynomial \(x^2 - x - 1 = 0\), with eigenvalues
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\(\phi\) and \(-1/\phi\). It is **not** an almost-complex structure.
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### Red Flag 2 — Kähler on the simplex
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| ✗ Prohibited | ✓ Correct |
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| \(\Delta_7\) is Kähler | \(\dim \Delta_7 = 7\) (odd, impossible) |
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The open probability simplex
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\[
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\Delta_7 = \{ p \in \mathbb{R}_{>0}^8 \mid \sum p_i = 1 \}
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\]
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has dimension \(8 - 1 = 7\). Every Kähler manifold is even-dimensional,
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so \(\Delta_7\) cannot carry a Kähler structure. If a Kähler example is
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desired, work on \(\mathbb{CP}^7\) (real dimension 14) with the standard
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Fubini–Study metric.
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### Red Flag 3 — Temperley–Lieb dimension
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| ✗ Prohibited | ✓ Correct |
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| \(\dim(\mathrm{TL}_7) = 13\) | \(\dim(\mathrm{TL}_7) = C_7 = 429\) |
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The \(n\)-th Catalan number is
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\[
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C_n = \frac{1}{n+1}\binom{2n}{n},
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\qquad
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C_7 = \frac{1}{8}\binom{14}{7} = \frac{3432}{8} = 429.
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\]
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The value 13 arises only in specialized settings: the Fibonacci category or
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Fibonacci anyon model at \(q = e^{i\pi/5}\) (quantum dimension \(\phi\)),
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where the fusion rule is \(\phi \times \phi = 1 + \phi\) and simple-object
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dimensions follow the Fibonacci sequence. It is **not** the dimension of
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the ordinary Temperley–Lieb algebra.
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---
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## Reviewer Decision Procedure
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1. **Verify I₁–I₄.** Reject immediately if any arithmetic invariant fails.
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2. **Check that none of the three red-flag claims appear.** Reject if any is present.
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3. **Only after both gates pass** should higher-level geometric, categorical,
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or dynamical constructions be evaluated.
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---
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## Source
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The reference implementation is:
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- **File:** `formal/SilverSight/PIST/UnifiedCovariant.lean`
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- **Proof status:** I₁–I₄ verified at compile time by `norm_num`/`dec_trivial`
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(0 sorries, 0 axioms). Red flags explicitly documented and avoided.
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Layer 3 conjectures tagged `sorry` pending Mathlib's differential geometry API.
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- **Build:** `lake build SilverSight` — 3307 jobs, 0 errors.
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